Transcript Document

Nucleon Electro-Magnetic Form Factors
Kees de Jager
June 14, 2004
Thomas Jefferson National Accelerator Facility
Operated by the Southeastern Universities Research Association for the U.S. Department Of Energy
Introduction
• Form Factor
response of system to momentum transfer Q,
often normalized to that of point-like system
Examples:
→scattering of photons by bound atoms
→nuclear beta decay
→X-ray scattering from crystal
→electron scattering off nucleon
Thomas Jefferson National Accelerator Facility
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Nucleon Electro-Magnetic Form Factors
 Fundamental ingredients in “Classical” nuclear theory
• A testing ground for theories constructing nucleons from quarks and gluons
- spatial distribution of charge, magnetization
wavelength of probe can be tuned by selecting momentum transfer Q:
< 0.1 GeV2 integral quantities (charge radius,…)
0.1-10 GeV2 internal structure of nucleon
> 20 GeV2 pQCD scaling
Caveat: If Q is several times the nucleon mass (~Compton wavelength),
dynamical effects due to relativistic boosts are introduced, making physical
interpretation more difficult
 Additional insights can be gained from the measurement of the form factors of
nucleons embedded in the nuclear medium
- implications for binding, equation of state, EMC…
- precursor to QGP
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Campaigns and Performance Measures
How are nucleons made from quarks and gluons?
The distribution of u, d, and s quarks in the hadrons
(the spatial structure of charge and magnetization in the nucleons is
an essential ingredient for conventional nuclear physics; the flavor
decomposition of these form factors will provide new insights and
a stringent testing ground for QCD-based theories of the nucleon)
DOE Performance Measures
2010 Determine the four electromagnetic form factors of the nucleon to
a momentum-transfer squared, Q2, of 3.5 GeV2 and separate the
electroweak form factors into contributions from the u,d and squarks for Q2 < 1 GeV2
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Formalism
Sachs Charge and Magnetization Form Factors GE and GM
 GE2   GM2

d
2
2
( E, q )   M 
 2 GM tan q / 2  
d
 1 

 2 E 'cos2 q / 2
M 
4 E 3 sin 4 q / 2
with E (E’) incoming (outgoing) energy, q scattering angle,
k anomalous magnetic moment
In the Breit (centre-of-mass) frame the Sachs FF can be written
as the Fourier transforms of the charge and magnetization
radial density distributions
GE and GM are often alternatively expressed in the Dirac (non-spin-flip) F1
and Pauli (spin-flip) F2 Form Factors
F1  GE   GM
G  GE
F2  M
k (1   )
Q2
=
4 M2
Thomas Jefferson National Accelerator Facility
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The Pre-JLab Era
• Stern (1932) measured the proton magnetic moment µp ~ 2.5 µDirac
indicating that the proton was not a point-like particle
• Hofstadter (1950’s) provided the first measurement of the proton’s
radius through elastic electron scattering
• Subsequent data (≤ 1993) were based on:
Rosenbluth separation for proton,
severely limiting the accuracy for GEp at Q2 > 1 GeV2
• Early interpretation based on Vector-Meson Dominance
• Good description with phenomenological dipole form factor:
2
  
GD   2
2 
  Q 
2
wi th   0.84GeV
corresponding to r (770 MeV) and w (782 MeV) meson resonances
in timelike region and to exponential distribution in coordinate space
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Global Analysis
P. Bosted et al.
PRC 51, 409 (1995)
æ
G = G = çç1 +
çè
p
E
p
M
æ
n
GM = çç1 +
çè
5
å
i= 1
ö
÷
ai Q ÷
÷
ø
i
ö
÷
åi= 1 biQ ø÷÷; GEn = 0
4
i
Three form factors very similar
GEn zero within errors -> accurate
data on GEn early goal of JLab
First JLab GEp proposal rated B+!
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Modern Era
Akhiezer et al., Sov. Phys. JETP 6 (1958) 588 and
Arnold, Carlson and Gross, PR C 23 (1981) 363
showed that:
accuracy of form-factor measurements can be significantly improved by
measuring an interference term GEGM through the beam helicity
asymmetry with a polarized target or with recoil polarimetry
Had to wait over 30 years for development of
• Polarized beam with
high intensity (~100 µA) and high polarization (>70 %)
(strained GaAs, high-power diode/Ti-Sapphire lasers)
• Beam polarimeters with 1-3 % absolute accuracy
• Polarized targets with a high polarization or
• Ejectile polarimeters with large analyzing powers
Thomas Jefferson National Accelerator Facility
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Pre-Jlab Measurements of GEn
No free neutron target available, early experiments used deuteron
Large systematic errors caused by subtraction of proton contribution
Elastic e-d scattering
(Platchkov, Saclay)
d
Qr
2
p
n 2
2
2
 {A  Bt an (qe/ 2)} (GE  GE )  [u (r)  w (r)]j0 ( )dr  ....
d
2
Yellow band represents range of
GEn-values resulting from the use
of different NN-potentials
Thomas Jefferson National Accelerator Facility
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Double Polarization Experiments to Measure GnE
• Study the (e,e’n) reaction from a polarized ND3 target
limitations: low current (~80 nA) on target
deuteron polarization (~25 %)
• Study the (e,e’n) reaction from a LD2 target and
measure the neutron polarization with a polarimeter
limitations: Figure of Merit of polarimeter
• Study the (e,e’n) reaction from a polarized 3He target
limitations: current on target (12 µA)
target polarization (40 %)
nuclear medium corrections
GEn
A^
=
GMn
A||
t + t ( 1+ t )tan2 (q / 2)
Thomas Jefferson National Accelerator Facility
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Neutron Electric Form Factor GEn
Galster:
a parametrization
fitted to old (<1971)
data set of very
limited quality
For Q2 > 1 GeV2
data hint that GEn has
similar Q2-behaviour
as GEp
Thomas Jefferson National Accelerator Facility
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Measuring GnM
Old method: quasi-elastic scattering from 2H
large systematic errors due to subtraction of proton contribution
d 3 (eD  e'n(p))
dE' de ' dn
• Measure (en)/(ep) ratio
RD  3
d  (eD  e' p(n))
Luminosities cancel
Determine neutron detector efficiency
dE'd e' d p
• On-line through e+p->e’+π+(+n) reaction (CLAS)
• Off-line with neutron beam (Mainz)
• Measure inclusive quasi-elastic scattering off polarized 3He (Hall A)
cosq vT ' RT '  2sinq cos vTL ' RTL ' 
*
A
*
*
v L RL  v T RT
RT’ directly sensitive to (GMn)2
Thomas Jefferson National Accelerator Facility
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Measurement of GnM at low Q2
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Preliminary GnM Results from CLAS
Thomas Jefferson National Accelerator Facility
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Early Measurements of GEp
•
•
•
relied on Rosenbluth separation
measure d/d at constant Q2
GEp inversely weighted with Q2, increasing the systematic error
above Q2 ~ 1 GeV2
1  E  E,q 
e

 R Q2 , e  e  1  
 {GMp Q2 }2  {GEp Q2 }2
   E '  Mott

Q2 = 4EE' sin2 ( q / 2 ) e 
1
1  2(1   )tan 2 (q / 2)
At 6 GeV2 R changes by only 8%
from e=0 to e=1 if GEp=GMp/µp
Hence, measurement of Gep with
10% accuracy requires 1.6%
cross-section measurements over
a large range of electron energies
Thomas Jefferson National Accelerator Facility
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Spin Transfer Reaction 1H(e,e’p)
Pn = 0
± hPt =
h 2 t ( 1 + t ) GEp GMp tan (qe / 2) / I 0
2
± hPl = ± h (Ee + Ee' )(GMp )
2
t ( 1 + t ) tan 2 ( qe / 2 ) / M / I 0
2
I 0 = {GEp (Q 2 )} + t {GMp (Q 2 )}
p
E
p
M
é1 + 2( 1 + t )tan 2 ( qe / 2 )ù
êë
ú
û
P E + Ee'
G
=- t e
tan( qe / 2 )
G
Pl 2M
No error contributions from
• analyzing power
• beam polarimetry
Thomas Jefferson National Accelerator Facility
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JLab Polarization-Transfer Data
•
•
•
E93-027 PRL 84, 1398 (2000)
Used both HRS in Hall A with FPP
E99-007 PRL 88, 092301 (2002)
used Pb-glass calorimeter for electron
detection to match proton HRS
acceptance
Reanalysis of E93-027 (Pentchev)
Using corrected HRS properties
→Clear discrepancy between polarization
transfer and Rosenbluth data
→Investigate possible source, first by
doing optimized Rosenbluth experiment
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Super-Rosenbluth (E01-001) 1H(e,p)
J. Arrington and R. Segel
• Detect recoil protons in HRS-L to diminish
sensitivity to:
• Particle momentum and angle
• Data rate
• Use HRS-R as luminosity monitor
• Very careful survey
• Careful analysis of background
MC simulations
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Rosenbluth
Pol Trans
Rosenbluth Compared to Polarization Transfer
• John Arrington performed detailed reanalysis of SLAC data
• Hall C Rosenbluth data (E94-110, Christy) in agreement with SLAC data
• No reason to doubt quality of either Rosenbluth or polarization transfer data
→Investigate possible theoretical sources for discrepancy
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Two-photon Contributions
Guichon and Vanderhaeghen (PRL 91 (2003)
142303) estimated the size of two-photon
effects (TPE) necessary to reconcile the
Rosenbluth and polarization transfer data
2
2

˜
˜

G
G
d

 M   e E 2  2e  
d
 
G˜ M


Pt
2e 
G˜ E 
2e

 ˜  1
Pl
 (1 e ) GM  1  e

G˜ E
G˜ M


2 
Y2 ( ,Q )




G˜ E 
2 
Y2 ( ,Q )
G˜ M 


Need ~3% value for Y2 (6% correction to eslope), independent of Q2, which yields minor
correction to polarization transfer
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Two-Photon Contributions (cont.)
Blunden et al. have calculated elastic contribution of TPE
Resolves ~50% of discrepancy
Chen et al., hep/ph-0403058
Model schematics:
• Hard eq-interaction
• GPDs describe quark
emission/absorption
• Soft/hard separation
• Assume factorization
Polarization transfer
1+2(hard)
1+2(hard+soft)
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Experimental Verification of TPE contributions
Experimental verification
• non-linearity in e-dependence
(test of model calculations)
• transverse single-spin asymmetry
(imaginary part of two-photon
amplitude)
• ratio of e+p and e-p cross section
(direct measurement of two-photon
contributions)
CLAS proposal PR04-116 aims at a
measurement of the e-dependence for
Q2-values up to 2.0 GeV2
Thomas Jefferson National Accelerator Facility
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Reanalysis of SLAC data on GMp
E. Brash et al., PRC submitted,
have reanalyzed SLAC data
with JLab GEp/GMp results
as constraint, using a similar
fit function as Bosted
Reanalysis results in 1.5-3%
increase of GMp data
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Theory I
→ Vector Meson Dominance
•
•
•
Photon couples to nucleon exchanging vector meson (r,w,f
Adjust high-Q2 behaviour to pQCD scaling
Include 2π-continuum in finite width of r
Lomon
3 isoscalar, isovector poles, intrinsic core FF
Iachello
2 isoscalar, 1 isovector pole, intrinsic core FF
Hammer
4 isoscalar, 3 isovector poles, no additional FF
→ Relativistic chiral soliton model
•
•
Holzwarth
Goeke
one VM in Lagrangian, boost to Breit frame
NJL Lagrangian, few parameters
→ Lattice QCD (Schierholz, QCDSF)
quenched approximation, box size of 1.6 fm, mπ = 650 MeV
chiral “unquenching” and extrapolation to mπ = 140 MeV (Adelaide)
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Vector-Meson Dominance Model
charge
magnetization
proton
neutron
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Theory II
• Relativistic Constituent Quark Models
Variety of q-q potentials (harmonic oscillator, hypercentral, linear)
Non-relativistic treatment of quark dynamics, relativistic EM currents
• Miller: extension of cloudy bag model, light-front kinematics
wave function and pion cloud adjusted to static parameters
• Cardarelli & Simula
Isgur-Capstick oge potential, light-front kinematics
constituent quark FF in agreement with DIS data
• Wagenbrunn & Plessas
point-form spectator approximation
linear confinement potential, Goldstone-boson exchange
• Giannini et al.
gluon-gluon interaction in hypercentral model
boost to Breit frame
• Metsch et al.
solve Bethe-Salpeter equation, linear confinement potential
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Relativistic Constituent Quark Model
charge
magnetization
proton
neutron
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High-Q2 behaviour
Basic pQCD scaling (Bjørken) predicts
F1  1/Q4 ; F2  1/Q6
 F2/F1  1/Q2
Data clearly do not follow this trend
Schlumpf (1994), Miller (1996) and
Ralston (2002) agree that by
• freeing the pT=0 pQCD condition
• applying a (Melosh) transformation to a
relativistic (light-front) system
• an orbital angular momentum component
is introduced in the proton wf (giving up
helicity conservation) and one obtains
 F2/F1  1/Q
• or equivalently a linear drop off of
GE/GM with Q2
Brodsky argues that in pQCD limit nonzero OAM contributes to F1 and F2
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High-Q2 Behaviour (cont)
Belitsky et al. have included logarithmic corrections in pQCD limit
Solid: proton
open: neutron
They warn that the observed scaling could very well be precocious
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Low-Q2 Behaviour
All EMFF allow shallow minimum (max for GEn) at Q ~ 0.5 GeV
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Pion Cloud
• Kelly has performed simultaneous fit to all
four EMFF in coordinate space using
Laguerre-Gaussian expansion and first-order
approximation for Lorentz contraction of
local Breit frame
2
2
Q2
 Q 
2
2
˜
GE,M (k)  GE,M (Q )1   with k 
and  
2M 
1 
• Friedrich and Walcher have performed a
similar analysis using a sum of dipole FF
for valence quarks but neglecting the
Lorentz contraction
• Both observe a structure in the proton and
neutron densities at ~0.9 fm which they
assign to a pion cloud
_
• Hammer et al. have extracted the pion cloud assigned to the NN2π
component which they find to peak at ~ 0.4 fm
Thomas Jefferson National Accelerator Facility
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Summary
• Very successful experimental program at JLab on nucleon form factors
thanks to development of polarized beam (> 100 µA, > 75 %), polarized
targets and polarimeters with large analyzing powers
• GEn
3 successful experiments, precise data up to Q2 = 1.5 GeV2
• GMn
Q2 < 1 GeV2 data from 3He(e,e’) in Hall A
Q2 < 5 GeV2 data from 2H(e,e’n)/2H(e,e’p) in CLAS
• GEp
Precise polarization-transfer data set up to Q2 =5.6 GeV2
New Rosenbluth data from Halls A and C confirm SLAC data
• Strong support from theory group on two-photon corrections, making
progress towards resolving the experimental discrepancy between
polarization transfer and Rosenbluth data
• Accurate data will become available at low Q2 on GEp and GEn from BLAST
• JLab at 12 GeV will make further extensions to even higher Q2 possible
Thomas Jefferson National Accelerator Facility
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